Quantum Mechanics demystified, a try
Galileo, Kopernikus, Keppler and Newton were some of the main conductors on composing classical formula for gravity:
$F=G\frac{m_1m_2}{r^2}$
I.e force of gravity between two objects at distance r of each other is their masses timed together, then divided by the square of their distance and finally multiplying all this by gravitational constant G.
To end up on this took centuries. Prompt observations, calculations and deductions were made on planets, their orbits, orbiting times and more. Galileo was dropping whatever objects at Pisa and Newton used apples ;-) in his intuitions. All that in spirit described in Characteristics of physics exploration
In early days value for the gravitational constant G was estimated by first somehow figuring out the mass of the earth. This was mainly based on coming somehow up on the density of the earth. By guessing or otherwise.
Then simplified version of Newton’s law of potential energy $(F=mgh)$, found out empirically to be effective on ground, was used to calculate the effective force e.g. between an apple and the earth. When this force was placed on the universal law of gravity, together with apple’s mass and the estimate of earth’s mass, G could be calculated.
As even guesses were involved, values for G derived in this way were doomed to be pretty inaccurate.
It was only at round 1800s that experimental methods, tools and equipment in physics had become accurate and elegant enough to try something else.
Henry Cavendish was among the first ones to set up an experiment to try something.
He had a rod hanging horizontally from a very thin string of quarz. On both heads of the rod there were a smallish ball attached. Then two large balls were placed besides the small balls at a small distance. Small balls were attracted by the larger one, the rod turned a bit and Cavendish measured the force by which the quarz-string was trying to rotate. Now by setting all the values to universal law of gravitation, gravitational constant G was calculated. He ended up with $G=(6.7±0.6)10^{-11}$, which is not far at all from the current understanding, which is $G=6.67430 10^{-11}$.
However, Cavendish wasn’t after to determine the value of G. He was after trying to figure the density of earth instead, along with the mass of earth.
Thus he called his experiment ‘Weighing the world’.